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Slide Rules

Index by Purpose

While many slide rules were made as general calculating instruments, for multiplying numbers and solving equations with squares, cubes, trigonometric functions, and logarithms, many others were made to ease the calculations associated with a specific task. Click on items in the list below to see rules in the collection with an identifiable specialized purpose. For comparison, a few illustrative examples of all-purpose slide rules are shown under the link to General Calculation.

This rule has a cylindrical hollow brass drum, which is covered with paper printed with 40 A scales. The first A scale runs from 100 to 112; the fortieth runs from 946 to 100 to 105. The paper is also printed in italics on the right side: Patented by Edwin Thatcher [sic], C.E. Nov. 1st 1881. Divided by W. F. Stanley, London, 1882. A wooden handle is attached to each end of the drum, and the drum slides in both directions.

The drum fits inside an open rotating frame to which 20 brass slats are fastened. The slats are lined with cloth and covered with paper. The paper on each slat is printed with two B and two C scales. The first B scale runs from 100 to 112; the fortieth runs from 946 to 100 to 105. The first C scale runs from 100 to 334; the fortieth runs from 308 to 325. The frame is attached to a mahogany base, and the object is housed in a mahogany case. A paper label appears to have been removed from the top of the case.

A paper of directions and rules for operating THACHER'S CALCULATING INSTRUMENT is glued to the top front of the base. A metal tag attached to the top back of the base is engraved: Keuffel & Esser (/) New York. The front right corner of the frame is stamped with numbers: 57 and 35. Presumably one of these is the serial number, but which one is not clear. In either case, the low number and the shape of the frame suggest that this example is the earliest Thacher cylindrical slide rule in the collections. Model 1740 sold for $30.00 in 1887.

Robert B. Steffes of the U.S. Bureau of Labor Statistics donated this instrument to the Smithsonian in 1970.

See also MA*312866 and 1987.0107.08.

References: Wayne E. Feely, "Thacher Cylindrical Slide Rules," The Chronicle of the Early American Industries Association 50 (1997): 125–127; Catalogue of Keuffel & Esser (New York, 1887), 128. This was the first K&E catalog to list the model 1740.

This rule consists of an outer wooden cylinder that slides up and down and rotates. Two brass rings lined with felt are inside this cylinder. The cylinder is covered with paper marked with a single spiral logarithmic scale graduated into 7250 parts and having a length, according to the maker, of 500 inches (nearly 42 feet). Inside the outer cylinder is a longer wooden cylinder, covered with paper marked with decimal, conversion, and sine tables. A solid mahogany handle is at one end. A third cylinder of brass is inside the instrument. A brass index is screwed to the top of the handle. A second, longer brass index is screwed to the mahogany base and marked with a scale of equal parts used in finding logarithms.

The tables on the middle cylinder include: decimal equivalents of feet and inches in feet; decimal equivalents of quarter weights and pounds in hundredweights; decimal equivalents of ounces and pounds in fractions of a pound; decimal equivalents of pounds, shillings, and pence in fractions of a pound; decimal equivalents of pence in shillings; days of the year as a fraction of the year; decimal equivalents of subunits of an acre; properties of various metals and woods; decimal equivalents of minutes of a degree in degrees; the Birmingham wire gauge; various conversion factors (mostly for weights and measures); and natural sines.

The outer, sliding cylinder is marked near the top: FULLERS SPIRAL SLIDE RULE. Near the bottom is marked: ENTD. STATS. HALL; STANLEY, Maker, LONDON. The bottom is stamped: 1099. The top of the long brass index is engraved: 1099 (/) 98. According to Wayne Feely, these numbers indicate the instrument has serial number 1099 and was made in 1898.

George Fuller, professor of civil engineering at Queen's University in Belfast, Ireland, patented this instrument in 1878. The Stanley firm made about 14,000 Fuller's spiral slide rules over nearly one hundred years. According to Boyd's Directory of the District of Columbia, Fred A. Schmidt, vendor of draftsmen's supplies, moved from 504 9th Street N.W. to 516 9th Street, with a branch at 1722 Pennsylvania Avenue, between 1895 and 1900.

According to the donor, this example came from the family of her first husband, Fred Robert Troll (1920–1971), a sanitary engineer who attended Columbia University. The original purchaser may have been his father, Frank Troll, or his uncle, who was an artist who traveled frequently.

In 1881, Edwin Thacher, a "computing engineer" for the Keystone Bridge Company in Pittsburgh, Pennsylvania, received a patent for an improvement in slide rules. Thacher was a graduate of Rennselaer Polytechnic Institute who spent much of his career designing railway bridges. To assist in his calculations, he designed a cylindrical slide rule. Thacher's rule, though it fit on a desk, was equivalent to a conventional slide rule over 59 feet long. It had scales for multiplication and division and another scale, with divisions twice as large, for use in finding squares and square roots. But it had no trigonometric scales.

To produce his "calculating instrument," Thacher turned to the London firm of W. F. Stanley. The company even designed a special dividing engine for preparing the scales for the instrument. These were printed on paper sheets, which were pasted to the drum and the slats. In this example, the paper is also printed in italics on the right side: Patented by Edwin Thatcher [sic], C.E. Nov. 1st 1881. Divided by W. F. Stanley, London, 1882.

The drum is rotated with wooden handles. The cylinder of slats is held in place with a brass frame, which is affixed to a wooden base. A paper of DIRECTIONS AND RULES FOR OPERATING is lacquered to the front of the base. The rear of the base bears a small silver metal label engraved: Keuffel & Esser (/) New York. F. F. NICKEL is painted underneath the base.

Keuffel & Esser Company of New York sold versions of the Thacher cylindrical slide rule from at least 1883 until about 1950. There were two models, one with a magnifying glass (K&E model 1741, later K&E model 4013), and one without (K&E model 1740, later K&E 4012). This is a model 1740. The front right corner of the instrument's metal frame is engraved with the number 107. A paper K&E label on the inside lid of the instrument's mahogany case is marked in ink: 1740/661 (/) Thachers (/) Calculating (/)Instr. The top front of the bottom of the case is also carved with 661. In 1887, the model 1740 sold for $30.00.

Frank Ferdinand Nickel purchased this example around 1883 and donated it to the Smithsonian in 1945, through his son, Henry W. Nickel. The elder Nickel was born in Hanau, Germany, in 1857. He came to the United States around 1883 and worked as a mechanical engineer in New York, Ohio, Pennsylvania, and New Jersey. He also taught at Columbia University in the 1910s. He wrote Direct-Acting Steam Pumps (New York: McGraw-Hill, 1915).

This rule consists of an outer wooden cylinder that both slides up and down and rotates. Two brass rings lined with felt are inside this cylinder. The cylinder is covered with paper marked with a single spiral logarithmic scale graduated into 7,250 parts and having a length, according to the maker, of 500 inches (nearly 42 feet). This length permitted computations up to four or five significant digits.

Inside the outer cylinder is a longer wooden cylinder, covered with paper marked with decimal, conversion, and sine tables. A solid mahogany handle is at one end. A brass index is screwed to the top of the handle. A second, longer brass index is screwed to the mahogany base and marked with a scale of equal parts used in finding logarithms. A third, removable, nickel-plated brass cylinder is inside the instrument and attached to the base. There is no case.

The tables on the middle cylinder include: decimal equivalents of feet and inches in feet; decimal equivalents of quarter weights and pounds in hundredweights; decimal equivalents of ounces and pounds in fractions of a pound; decimal equivalents of pounds, shillings, and pence in fractions of a pound; decimal equivalents of pence in shillings; days of the year as a fraction of the year; decimal equivalents of subunits of an acre; properties of various metals and woods; decimal equivalents of minutes of a degree in degrees; the Birmingham wire gauge; various conversion factors (mostly for weights and measures); and natural sines.

The outer, sliding cylinder is marked near the top: FULLERS SPIRAL SLIDE RULE. Near the bottom is marked: ENTD. STATS. HALL; STANLEY, Maker, LONDON. The bottom is stamped: 1389. The top of the long brass index is engraved: 1389 (/) 1901. According to Wayne Feely, these numbers indicate the instrument has serial number 1389 and was made by Stanley in 1901. A white celluloid tag affixed to the handle reads: KEUFFEL & ESSER CO. (/) ST. LOUIS. CHICAGO. (/) NEW YORK. (/) U.S.A. In the 1901 Keuffel & Esser catalog, Fuller's Spiral Slide Rule is listed as Model 4015 and priced at $30.00.

See also MA*311958, 1998.0046.01, and MA*316575.

References: Wayne E. Feely, "The Fuller Spiral Scale Slide Rule," Chronicle of the Early American Industries Association 50, no. 3 (1997): 93–98; Catalogue of Keuffel & Esser (New York, 1901), 290; James J. Fenton, "Fuller's Calculating Slide-Rule," Transactions and Proceedings of the Royal Society of Victoria 22 (1886): 57–61; Dieter von Jezierski, Slide Rules: A Journey Through Three Centuries, trans. Rodger Shepherd (Mendham, N.J.: Astragal Press, 2000), 42–43; George Fuller, Instructions for the Use of the Fuller Calculator (London: W. F. Stanley & Co., Ltd., [about 1950]), http://www.mccoys-kecatalogs.com/KEManuals/4015/4015.htm. An 1879 first edition of the instructions manual was received with the instrument and is stored in the accession file.

In 1881, Edwin Thacher, a "computing engineer" for the Keystone Bridge Company in Pittsburgh, Pennsylvania, received a patent for an improvement in slide rules. Thacher, a graduate of Rennselaer Polytechnic Institute, spent much of his career designing railway bridges. To assist in his calculations, he designed a cylindrical slide rule. Thacher's rule, though it fit on a desk, was equivalent to a conventional slide rule over 59 feet long. The rule had scales for multiplication and division and another scale, with divisions twice as large, for use in finding squares and square roots. There were no trigonometric scales.

To produce his "calculating instrument," Thacher turned to the London firm of W. F. Stanley. The company even designed a special dividing engine for preparing the scales for the instrument. These were printed on paper sheets, which were pasted to the drum and the slats. In this example, the paper is also printed in italics on the right side: Patented by Edwin Thatcher [sic], C.E. Nov. 1st 1881. Divided by W. F. Stanley, London, 1882. Made by Keuffel & Esser Co. N.Y. Wayne Feely has suggested that K&E began manufacturing (as opposed to simply distributing) Thacher cylindrical slide rules in 1887, indicating 1887 is the earliest date for this example of the instrument.

The drum is rotated with wooden handles. The cylinder of slats is held in place with a brass frame, which is affixed to a wooden base. A paper of DIRECTIONS AND RULES FOR OPERATING is glued to the front of the base. A small silver metal tag affixed to the front right of the base is engraved: KEUFFEL & ESSER CO. (/) NEW-YORK (/) 589. A metal extension on the front, screwed to both sides of the frame, bears a fixed holder and thumbscrew that once held a magnifying glass.

A paper K&E label on the inside lid of the instrument's mahogany case is marked in ink: 1741/589 (/) Thacher's (/) Calculating (/) Instr. The inside of the lid and the bottom of the base are both painted: M59. The back of the base is missing a chip 5 cm in length. The left and right sides of the case both bear labels marked in ink: INSTRUMENT (/) CALCULATING (/) THATCHER. A diagonal line is drawn through the second T in "Thatcher" on the right side.

Keuffel & Esser Company of New York sold versions of the Thacher cylindrical slide rule from at least 1883 until about 1950. There were two models, one with a magnifying glass (K&E model 1741, K&E model 4013 after 1900), and one without (K&E model 1740, later K&E 4012). This is a model 1741. In 1892, the model 1741 sold for $40.00. The Physics Department of the United States Military Academy transferred this example to the Smithsonian in 1958.

This wooden instrument is faced on both sides with white celluloid that is attached with brass screws instead of glue. On one side are 20-inch scales: cosine and sine scales on the upper part of the base, two identical logarithmic scales (in three cycles) labeled TIME SCALE on the slide, and a tangent scale on the lower part of the base. The slide is in two pieces, so the second Time Scale may be removed and adjusted relative to the first Time Scale with the aid of a brass thumbscrew.

Three glass indicators are in three-sided brass frames, two on the upper part of the base and one on the lower part of the base. The top of the base is marked: J. HICKS (/) LONDON. It is also marked: PILOT BALLOON SLIDE RULE MO (O is superimposed on M) 505. MO is an abbreviation for Meteorological Office, and 505 may be a serial number. An inventory sticker on the back reads: DEPARTMENT OF AGRICULTURE (/) US. The inventory number has been cut away. The instrument fits in a wooden case covered with black leather and lined on one side with purple satin.

In the 20th century, the Meteorological Office of Great Britain used pilot balloon slide rules to convert azimuth and elevation readings (taken with theodolites during the ascent of a pilot balloon) into data on wind velocity and direction. James Joseph Hicks (1825–1916), who began supplying instruments to the Office in 1869, made the first pilot balloon slide rule in 1915 from a design by Francis John Welsh Whipple, the Superintendent of Instruments.

After Hicks died, W. F. Stanley & Co. took over manufacture of this rule, called the Mark I, but retained the Hicks name. Additional labels were placed on the scales, such as "Azimuth." By 1927, A. G. Thornton Ltd. and other firms were making the Mark II, which had one slide and four indicators. Production of the Mark I may have continued until 1938.

The U.S. Weather Bureau was a part of the U.S. Department of Agriculture until 1940, when it was transferred to the U.S. Department of Commerce. This instrument apparently was not adopted by American meteorologists, since the Bureau used the Keuffel & Esser polyphase duplex slide rule to convert observations. For examples of that type of slide rule, see MA*318476, MA*321778, and 1981.0933.03. For an American theodolite used to observe pilot balloons, see PH*308184.

This rule consists of an outer wooden cylinder that both slides up and down and rotates. Two brass rings lined with felt are inside this cylinder. The cylinder is covered with paper marked with a single spiral logarithmic scale graduated into 7,250 parts and having a length, according to the maker, of 500 inches (nearly 42 feet). Inside the outer cylinder is a longer wooden cylinder, covered with paper marked with decimal, conversion, and sine tables, and half-lined with felt. A solid mahogany handle is at one end. A brass index is screwed to the top of the handle. A second, longer brass index is screwed to the mahogany base and marked with a scale of equal parts used in finding logarithms. A third and removable brass cylinder is inside the instrument and attached to the base.

The tables on the middle cylinder include: decimal equivalents of feet and inches in feet; decimal equivalents of quarter weights and pounds in hundredweights; decimal equivalents of ounces and pounds in fractions of a pound; decimal equivalents of pounds, shillings, and pence in fractions of a pound; decimal equivalents of pence in shillings; days of the year as a fraction of the year; decimal equivalents of subunits of an acre; properties of various metals and woods; decimal equivalents of minutes of a degree in degrees; the Birmingham wire gauge; various conversion factors (mostly for weights and measures); and natural sines.

The outer, sliding cylinder is marked near the top: FULLERS SPIRAL SLIDE RULE. Near the bottom is marked: ENTD. STATS. HALL; STANLEY, Maker, LONDON. The bottom of the outer cylinder and the top of the long brass index are stamped: 858. According to Wayne Feely, the serial number 858 dates this instrument to 1895 or 1896.

The rule is in a rectangular mahogany case marked in script on the top: Calculator. A paper Keuffel & Esser label on the inside lid of the instrument's mahogany case is marked in ink: 1742 (/) Fuller's (/) Spiral (/) Slide Rule. Fuller's Spiral Slide Rule was first listed in Keuffel & Esser's 1895 catalog and sold for $28.00.

George Fuller, professor of civil engineering at Queen's University in Belfast, Ireland, patented this instrument in 1878. The Stanley firm made about 14,000 Fuller's spiral slide rules over nearly one hundred years, with K&E distributing a large share of the instruments sold in the United States. The Naval Engineering Division of the U.S. Coast Guard transferred this example to the Smithsonian in 1959. The Coast Guard engineers provided brief instructions:

"To calculate (5 X 6 X 4)/3 turn the outer cylinder until the first factor (5) is opposite the fixed pointer, set the slot in the movable indicator to read (0), turn the outer cylinder until the second factor (6) appears opposite the movable indicator. (The result will be found on the outer cylinder opposite the first indicator.) To multiply by the third factor (4), set the slot in the movable indicator to (0), turn the outer cylinder until the movable indicator indicates the third factor (4); (the result will be found opposite the fixed indicator.) To divide by (3) set the movable indicator to (3), turn outer cylinder until the slot in the movable indicator is (0) on the outer cylinder and the result will be found opposite the fixed pointer."

This instrument consists of a wooden base to which a flat rectangular scale printed on white celluloid is attached. The scale is divided logarithmically and arranged in 20 parallel lines. Each line is about five inches long. A wooden frame slides backward and forward over the base. Within this frame is a second frame, which has a clear celluloid window. Four index marks are drawn on the window. A loose metal wedge with a pin attached serves as a pointer, and it may be placed at any point on the window. The scales are marked: THE COOPER 100 INCH SLIDE RULE (/) PATENTED.

The feet of the base are lined with green felt. The instrument fits in a leather-covered cardboard box that is lined with white felt. A sticker inside the lid reads: WILLIAM DUBILIER (/) 72 Esplanade (/) NEW ROCHELLE, N. Y. There is also a note that reads: TELEPHONE, PARK 1081. (/) WIRELESS CALL, 5AU. (/) 94, ADDISON ROAD (/) KENSINGTON, W. 14. (/) 24/12/22 (/) To W. D. (/) With very best wishes for (/) Xmas and the New Year. (/) W.v.P.

William Dubilier (1888–1969), the donor of this instrument, was an American electrical engineer and inventor who received this instrument from a friend in Great Britain in 1922. By 1923, W. F. Stanley & Co. made this rule and stamped the outer frame with its mark. Although the rule worked well for multiplication and percentage problems, it was difficult to set the rule accurately for more complex calculations. At the relatively high price of £4, the instrument probably never sold widely. No patents for the device have been found. For the instruction manual, see MA*259739.01.